What is the general solution for cos(2x)+cos(4x)=0 ?

The general solution for cos(2x)+cos(4x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3

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cos(2x)+cos(4x)=0

cos (2 x) + cos (4 x) = 0

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

Solution steps

cos (2 x) + cos (4 x) = 0

Rewrite using trig identities

2 cos (3 x) cos (x) = 0

Solving each part separately

cos (3 x) = 0 or cos (x) = 0

cos (3 x) = 0 : x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}, x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Merge Overlapping Intervals

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

2 sin (\frac{x}{3}) = 1

sin^{2} (x) - 3 cos (x) = 3

sec (x) = \frac{2 3}{2}

6 sin (2 x) = 4

cos^{2} (x) + sin (x) = - 1

What is the general solution for cos(2x)+cos(4x)=0 ?
The general solution for cos(2x)+cos(4x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3